Lecture Notes: Quantum Mechanics and Orbitals

Introduction to Orbitals

• Orbital Definition: The most probable location to find an electron.
• Bohr Model of the Atom: Circular orbits representing energy levels.

Energy Levels and Quantum Numbers

• Principal Quantum Number (n)
  • Represents the energy level and size of the orbital.
  • As "n" increases, the distance from the nucleus increases.
  • Lower "n" values indicate electrons closer to the nucleus with lower energy.

Angular Momentum Quantum Number (L)

• Describes the shape of the orbital
  • L = 0: s orbital (spherical shape)
  • L = 1: p orbital (dumbbell shape)
  • L = 2: d orbital (cloverleaf shape)
  • L = 3: f orbital (complex shape)
• Sublevel Correspondence
  • L values determine sublevels: s, p, d, f

Relationship Between n and L

• L ≤ n-1
  • n = 1: Only s sub-level (L=0)
  • n = 2: S and P sub-levels (L=0, 1)
  • n = 3: S, P, and D sub-levels (L=0, 1, 2)
  • n = 4: S, P, D, and F sub-levels (L=0, 1, 2, 3)

Magnetic Quantum Number (M_L)

• Describes the orientation of the orbital
  • For s sub-level: L=0, hence M_L=0
  • For p sub-level: L=1, M_L varies between -1 and 1
  • For d sub-level: L=2, M_L varies between -2 and 2

Electron Spin Quantum Number (M_S)

• Electron Spin
  • Two possibilities: +1/2 (up spin) or -1/2 (down spin)
• Pauli’s Exclusion Principle
  • Each electron in an atom has a unique set of four quantum numbers.

Examples

• 2p₅ Electron Quantum Numbers

  • n = 2: Second energy level
  • L = 1: P sub-level
  • M_L = 0: Orientation within P sub-level
  • M_S = -1/2: Spin direction

• 3d₅ Electron Quantum Numbers

  • n = 3: Third energy level
  • L = 2: D sub-level
  • M_L = 2: Orientation within D sub-level
  • M_S = +1/2: Spin direction

Conclusion

• Engage with additional resources for further understanding.
• Recommended further videos on quantum numbers and electron configurations.

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